Case 1. Bushs Meat Company

Bushs Meat Company produces three products from original meatcanned meat, frozen meat, and ham meat. It purchases meat from three farms near the Great Lakes. The original meat is purchased at the farms and immediately converted into pure meat at plants at the farm sites and stored there in refrigerated tanks. The meat is then transported to four different plants in Virginia, Michigan, Tennessee, and Indiana, where it is processed into canned meat, frozen meat, and ham meat. Farms output typically differs each month in the harvesting season, and the plants have different processing capacities. In a particular month the farm in New York has 1,400 tons of unprocessed pure meat available, whereas the farm in Ohio has 1,500 tons and the farm in Pennsylvania has 1,300 tons. The processing capacity per month is 1,200 tons of pure meat at the plant in Virginia, 1,100 tons of meat at the plant in Michigan, 1,400 tons at the plant in Tennessee, and 1,400 tons at the plant in Indiana. The cost per ton of transporting pure meat from the farms to the plant is as follows:

plant

Vineyard

Virginia

Michigan

Tennessee

Indiana

New York

$1000

$720

$900

$750

Pennsylvania

970

800

1,050

880

Ohio

900

830

780

820

The plants are different ages, have different equipment, and have different wage rates; thus, the cost of processing each product at each plant ($/ton) differs, as follows:

product

plant

Virginia

Michigan

Tennessee

Indiana

canned meat

$2,000

$2,350

$2,200

$1,900

ham meat

4,100

4,200

3,950

3,900

frozen meat

2,600

2,300

2,500

2,800

This month the company needs to process a total of 1,200 tons of canned meat, 900 tons of frozen meat, and 700 tons of ham meat at the four plants combined. However, the production process for canned meat results in some meat lose, and the process for ham includes a roasting stage that evaporates water content. To process 1 ton of ham meat requires 2 tons of pure meat; 1 ton of canned meat requires 1.5 tons of pure meat; and 1 ton of frozen meat requires 1 ton of pure meat.

Bushs management wants to determine how many tons of pure meat to ship from each of the farms to each of the plants and the number of tons of each product to process at each plant. Thus, management needs a model that includes both the logistical aspects of this problem and the production processing aspects. It wants a solution that will minimize total costs, including the cost of transporting pure meat from the farms to the plants and the product processing costs. Help Bushs solve this problem by formulating a linear programming model and solve it by using the computer.

1) Build a linear programming model.

2) Solve the model using Excel Solver.